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 yufeizhao.com
The number of independent sets in an irregular graph
| | gilkalai.wordpress.com
Micha Perles' Geometric Proof of the Erdos-Sos Conjecture for Caterpillars | Combinatorics and more
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| | A geometric graph is a set of points in the plane (vertices) and a set of line segments between certain pairs of points (edges). A geometric graph is simple if the intersection of two edges is empty or a vertex of both. A geometric graph is convex if the vertices are in convex position. A...
| | 11011110.github.io
A binary model of cycle 3-coloring
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| | 3-colorings of graphs are inherently a ternary thing, right? There are three choices for the color of each vertex. But, for 3-colorings of cycles, there's a ...
| | yufeizhao.wordpress.com
Extremal regular graphs | Yufei Zhao
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| | This post is adapted from my new expository survey Extremal regular graphs: independent sets and graph homomorphisms. The earliest result in extremal graph theory is usually credited to Mantel, who proved, in 1907, that a graph on $latex {n}$ vertices with no triangles contains at most $latex {n^2/4}$ edges, where the maximum is achieved for...
| | jhui.github.io
"Deep learning - Computation & optimization."
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| [AI summary] The provided text discusses various mathematical and computational concepts relevant to deep learning, including poor conditioning in matrices, underflow/overflow in softmax functions, Jacobian and Hessian matrices, learning rate optimization using Taylor series, Newton's method, saddle points, constrained optimization with Lagrange multipliers, and KKT conditions. These concepts are crucial for understanding numerical stability, optimization algorithms, and solving constrained problems in machine learning.